This weekend I was able to successfully use "coconut Pete's old t-shirt method"
I was doing the cheap version of DangerMouse's way and just trying to use a plunger on the drain, but it just kept shooting air out of the tub overflow.
For CoconutPete's old t-shirt method you need:
Philips head screw driver
Turn on the water in the tub
Throw the old t-shirt into the tub
Remove the 2 screws from the tub overflow and remove the cover.
Grab the old t-shirt and wring it out.
Shove the old t-shirt into the overflow pipe, effectively plugging it.
Plunge the drain!
Watch in amazement as the drain now works.
At least it worked for me.